Jing-chun FENG*, Ya-fang REN, Zhong-nan DUAN, Zhan-jun LIU, Hai-yang LI

1. Institute of Project Management Informationization, Business School, Hohai University, Nanjing 211100, P. R. China

2. Construction and Administration Bureau of South-to-North Water Diversion Middle Route Project, Beijing 100053, P. R. China

Penalty model for delay of bidding section construction period in South-to-North Water Diversion Eastern Route Project from perspective of programs

Jing-chun FENG*1, Ya-fang REN1, Zhong-nan DUAN1, Zhan-jun LIU2, Hai-yang LI2

1. Institute of Project Management Informationization, Business School, Hohai University, Nanjing 211100, P. R. China

2. Construction and Administration Bureau of South-to-North Water Diversion Middle Route Project, Beijing 100053, P. R. China

According to the multi-project and program management theory, this paper analyzes the program generation principle and establishes a program based on progress goals. On the basis of the present situation of calculation of penalty for delay of the bidding section construction period with the critical path method, we studied the effects of contractor-induced delay of the bidding section construction period in detail, including the effects on the construction period of the bidding section itself, the earliest start times of the next bidding section and other subsequent bidding sections, and the construction period of the program, and then constructed a penalty model for delay of the bidding section construction period from the perspective of programs. Using the penalty model, we conducted a practical analysis of penalty for delay of the construction period of the Baoying station program in the South-to-North Water Diversion Project. The model can help determine the amount of penalty for delay of the construction period in bidding sections scientifically and reasonably.

program establishment; program management; bidding section construction period; critical path method (CPM); penalty model; South-to-North Water Diversion Project

1 Introduction

Program management is one of the main contents of large and medium-sized project management. Progress goal control of large and medium-sized projects is one of the important ways to achieve strategic objectives. There is a close relationship between progress goals and strategic objectives, and strategic objectives determine progress goals. Strategic objectives are composed of general goals and sub-goals. In order to achieve the strategic objectives of different levels, large and medium-sized projects need to be decomposed into work breakdown structures corresponding to the strategic objectives of different levels; therefore large andmedium-sized projects are a typical multi-project system. Considering the close relations between progress goals and strategic objectives and such factors as multiple levels of progress goals, high requirements for the construction period and project completion rate, and strong conditionality between the progress goals of different levels of large and medium-sized projects, it is necessary to control the progress goals of different levels, especially those of higher levels. Progress goals of higher levels often depend on multi-projects; therefore, program management is necessary, and penalty for delay of the construction period is one of the measures to control the progress goals.

The existing methods for calculation of penalty for construction delay are suitable for a single project but cannot solve multi-project problems effectively. A single project consists of several pieces of work that coordinate with each other. If a piece of work is delayed, the delay time can be made up by accelerated construction; even if it cannot be offset completely, it only influences the schedule of itself. However, for large and medium-sized projects, program schedule management with the basic unit placed on progress goals of bidding sections is more important, and the progress goals of the program are related to different contractors, who take charge of different bidding sections. Compared with a single project, it is difficult to remove the impact of delay in bidding sections by accelerated construction. When the delay in a bidding section influences not only the construction period of itself but also the earliest start times of the next bidding section and other subsequent bidding sections and the construction period of the program, the claims include the following parts: the employer’s claim for the delayed bidding section itself, the contractors’ claims for the impacts on the next bidding section and other subsequent bidding sections, and the employer’s claim for the influence on the program. If the delay in a bidding section does not exceed its free float, it does not influence the earliest start time of the next bidding section; if it does not exceed its total float, it does not influence the construction period of the program. Thus, the influences of delay in bidding sections on a program are complex, and it is necessary to study the penalty for delay of the bidding section construction period in different situations.

Some scholars have performed research as follows: Wang and Yang (2005) developed methods to optimize multi-contract incentive and chose the optimal construction period by establishing a leader-follower hierarchical decision model to keep the balance between the employer and contractor. He et al. (2005) solved the problems of project payment schedule with reward and punishment structures, and constructed a reward and punishment model based on time and payment. Zheng (2008) investigated the project incentive mechanism from the perspective of quality, safety, and schedule. The existing research focuses on the construction period incentive mechanism of a single project. However, there are few research and achievements on penalty for delay of the bidding section construction period from the perspective of programs.

While in practical analysis, the penalty model for delay of the bidding sectionconstruction period mainly relies on the relevant provisions (FIDIC 1999) and engineering practical experiences. According to the current penalty calculation method, a fixed penalty rate is taken, and the penalty for delay of the bidding section construction period is equal to the penalty rate multiplied by the contract amount. The method is only suitable for the case of a single project’s contract but not suitable for program cases. The reasons are as follows: on the one hand, the penalty calculation method only considers the loss caused by the delay in a bidding section itself but does not consider the effects on the earliest start times of the next bidding section and other subsequent bidding sections; on the other hand, it does not consider the impact on the construction period of the program. In the program case, the degree of influence on the program caused by delay in a bidding section only depends on days of delay but has nothing to do with the contract amount of the bidding section. However, according to the current penalty calculation method, the penalty for delay of the bidding section construction period depends on both the contract amount and penalty rate, which can not reflect the influence of the delay in the bidding section on the program objectively, and obviously, the amount of penalty calculated with the current penalty calculation method is unreasonable.

Progress goals of a program will directly influence the realization of strategic objectives, and it is necessary to establish a penalty model for delay of the bidding section construction period based on the analysis of the influences of progress goals of the bidding sections on those of the program. In this study, through analysis of the progress goal system of large and medium-sized projects and construction of programs, we adopted the program management theory and the critical path method to establish a penalty model for delay of the bidding section construction period, and applied the penalty model to the Baoying station program in the South-to-North Water Diversion Project.

2 Program based on progress goals

2.1 Definition of program

A program is a group of projects with common objectives, including the functional and controlling objectives, which cannot be achieved by a single project or part of projects, and the loss or failure of any project may lead to the failure of the common objectives. According to this definition, the division standards of a program should be common objectives; therefore, the components of a program are associated with each other. There are two kinds of programs: one consists of a group of relevant projects that have common objectives; the other is a combination of a series of purposeful and changeable activities. With the progress goal system, it is possible to establish programs with respect to different levels of progress goals (Feng et al. 2010, 2011; Reiss et al. 2006; Turner et al. 2000). The construction period of programs is so important that it will directly influence the realization of the corresponding strategic objectives. Thus, attention should be paid to the following two points: one is the influences of theconstruction periods of single projects or bidding sections on those of the program; the other is the interactions between single projects or between bidding sections.

2.2 Generation of program based on progress goals

According to the work breakdown structure, generally, large and medium-sized projects can be classified into stage projects, individual projects, bidding sections, and pieces of work. Accordingly, the progress goal system of large and medium-sized projects usually includes four levels: level 1 is the progress goal of different stage projects; level 2 is the progress goal of individual projects, which is also called the controlling goal; level 3 is the progress goal of bidding section schedules, which is also called the guiding objective; and level 4 is the progress goal of pieces of work, which is also called the implemental progress goal. According to the definition and the construction principle of the programs, it is possible to generate programs of large and medium-sized projects based on the progress goal system: the program corresponding to the progress goal of level 1 is composed of different stage projects; the program corresponding to the progress goal of level 2 is composed of different individual projects included in each stage project; the program corresponding to the progress goal of level 3 is composed of different bidding sections included in each individual project; and the program corresponding to the progress goal of level 4 is composed of different pieces of work included in each bidding section.

3 Penalty model for delay of bidding section construction period

Programs corresponding to progress goals of levels 1, 2, 3, and 4 focus on different projects. The penalty model for delay in bidding sections corresponding to the progress goal of level 3 is discussed in this paper.

3.1 Influence of delay of bidding section construction period on programs

In order to calculate the amount of penalty for delay in a bidding section scientifically, it is necessary to analyze the influence of delay in the bidding section on the program, which probably includes the influence on its own construction period, the earliest start times of the next bidding section and other subsequent bidding sections, and the construction period of the program. Based on that, the penalty model is constructed, and the influence can be quantified by means of the losses caused by the delay in different aspects of the program (Browning 2001; Bubshait 2003; Pillai et al. 2002; Tareghian and Taheri 2006; Woodbine 2004; Broome and Perry 2002).

3.2 Construction of penalty model

3.2.1 Steps of model construction

According to the critical path analysis and the program principle, if a delay takes place in a bidding section on the critical path, it will prolong the construction period of the programinevitably. For non-critical bidding sections, if the delay in a bidding section exceeds its total float, it will influence the construction period of the program. Therefore, through analyzing the actual delay time, free float, and total float of the critical and non-critical bidding sections, it is possible to construct a penalty model for delay of the bidding section construction period. The steps of model construction are as follows:

(1) According to the duration of the bidding sections and the mutual logical relationships between them, a double code network diagram for the program of bidding sections is drawn.

(2) The critical path and the construction period of bidding sections are calculated and determined.

(3) The total float and free float of each bidding section are calculated.

(4) Based on the actual completion date and the delay time of each bidding section, the influence of delay in each bidding section on the program is analyzed.

(5) According to the relationships between the actual delay time, the free float, and the total float of the bidding section, the penalty model for delay of the bidding section construction period is constructed for the following cases: (a) the actual delay time is less than or equal to the free float, (b) the actual delay time is more than the free float but less than or equal to the total float, and (c) the actual delay time is more than the total float.

(6) For a given bidding section program, various losses of the program caused by delay in bidding sections are analyzed and calculated.

3.2.2 Analysis of delay in bidding sections from perspective of programs

Supposing that the number of bidding sections of a program isn, and the actual delay time of theith bidding section isTi, the influences of delay in bidding sections are analyzed.

3.2.2.1 Analysis of delay in bidding sections on critical path

If a bidding section on the critical path is delayed, it will influence the program in the following aspects: the earliest completion time of itself, the earliest start times of the next bidding section and other subsequent bidding sections, and the construction period of the program.

3.2.2.2 Analysis of delay in bidding sections on non-critical path

If a bidding section on the non-critical path is delayed, the influence on the program caused by the delay should be analyzed in three cases:

(1) If 0＜Ti≤FFi, whereFFiis the free float of theith bidding section, the delay in theith bidding section only influences the construction period of itself, but has no influence on the earliest start times of the next bidding section and other subsequent bidding sections and the construction period of the program.

(2) IfFFi＜Ti≤FTi, whereFTiis the total float of theith bidding section, the delay in theith bidding section influences not only the construction period of itself, but also the earliest start times of the next bidding section and other subsequent bidding sections. It has no influence on the construction period of the program.

(3) IfTi＞FTi, the delay of theith bidding section influences not only the construction period of itself, but also the earliest start times of the next bidding section and other subsequent bidding sections and the construction period of the program.

3.2.3 Penalty function for delay of bidding section construction period from perspective of programs

Considering the influence of delay in bidding sections on the critical and non-critical paths on the program, the penalty function for delay in bidding sections of the program is constructed.

3.2.3.1 Penalty function for delay in bidding sections on non-critical path

If a bidding section on the non-critical path is delayed by the contractor, the penalty function for delay in the bidding section is as follows:

wheref(Ti) is the penalty function;Ciis the amount of claim from the employer against the contractor of theith bidding section for its delay in the bidding section;Ci+kis the amount of claim from the contractor of thekth subsequent bidding section against the employer for delaying the construction period of theith bidding section, andk=1, 2,…,n?i; andCtis the amount of claim from the employer against the contractor of theith bidding section for delaying the program resulted from the delay in theith bidding section.

3.2.3.2 Penalty function for delay in bidding sections on critical path

If a bidding section on the critical path is delayed by the contractor, it will inevitably influence the earliest start times of the next bidding section and other subsequent bedding sections and the construction period of the program. The penalty function for delay of the construction period in the bidding section included in the program is derived as follows:

4 Practical analysis of penalty for delay in Baoying station program in South-to-North Water Diversion Project

The South-to-North Water Diversion Project is a complex large-scale project composed of numerous construction projects. Establishing an effective penalty model can help control the progress goals effectively. According to the work breakdown structure and objective decomposition system of the South-to-North Water Diversion Project, a program system of the South-to-North Water Diversion Project was constructed based on the progress goals. The Baoying station program belongs to the progress goal of level 3 of the South-to-North WaterDiversion Eastern Route Project, which is composed of 14 bidding sections, including the housing project of control station (E), the green plant project of control station (N), civil construction and equipment installation (A), the Yanghuai Road (J), building construction and decoration engineering (M), pump and its affiliated equipment (B), motor and its affiliated equipment (C), sets of high- and low-voltage electrical equipment of 10 kV or below (L), sets of electrical cables with voltage lower than 11 kV (H), sewage disposal equipment manufacturing (G), bridge crane manufacturing (F), GIS switch group (I), main transformer (D), and microcomputer monitoring and video surveillance system (K). In this study, we conducted practical analysis of the penalty model from the perspective of the Baoying station program.

4.1 Amounts of penalty obtained by current penalty calculation method

The planned construction period, actual construction period, and contract amount of each bidding section of the Baoying station program and the penalty for delay in each bidding section that was calculated with the current penalty calculation method are listed in Table 1.

Table 1 Penalty for delay in bidding sections of Baoying station program calculated with current penalty calculation method

The calculation of the amounts of penalty for the Baoying station program with the current penalty calculation method obeys the following rules: the penalty for delay of the principal projects is 0.5% per day of the contract amount; the penalty for delay of projects related to equipment fabrication and installation is 0.2% per day of the contract amount. The amount of penalty for delay of a bidding section is the product of the days of delay, the contract amount, and the penalty ratio of the bidding section. The highest amount of penalty is5% of the contract amount.

The problems in the current penalty calculation method for the Baoying station program are as follows: it does not consider the effects of delay in bidding sections on the earliest start times of the next bidding section and other subsequent bidding sections and the construction period of the program, and the penalty rate is predetermined. It is too simple and subjective, and lacks quantitative models; moreover, the calculation of the penalty for delay in bidding sections based on the contract amount is not in accordance with the actual situation from the perspective of programs.

4.2 Amounts of penalty obtained by present penalty model

By drawing the network planning diagram of the Baoying station program and calculating the time parameters, the critical path was found, which is A-D-H-I-K-N. Meanwhile, the total float and free float of each bidding section can be calculated with the critical path method. The network planning diagram and related parameters are shown in Fig. 1. The data in the left column of the tables are the earliest start time and earliest finish time of each bidding section, the data in the middle column are the latest start time and latest finish time of each bidding section, and the data in the right column are the total float and free float of each bidding section. The data in parentheses are the planned construction period of each bidding section, and the data in circles are the serial number of nodes. The solid line indicates the real construction process, and the dotted line indicates the virtual construction process.

Fig. 1 Network planning diagram of bidding sections of Baoying station program

With the data of investigation, delayed bidding sections were determined under different constraints. The penalty for delay of bidding section construction periods is calculated with the present penalty model. According to the location of bidding sections and the loss of the program caused by delay of the construction period, the delays in bidding sections are classified into two kinds: the delay in critical bidding sections and the delay in non-criticalbidding sections. Of all the critical bidding sections, sections D, H, and I are delayed, and the delay in these projects influences not only the construction period of themselves, but also the earliest start times of the next bidding section and other subsequent bidding sections and the construction period of the program. Of all the non-critical bidding sections, six bidding sections are delayed, in which the delay times of sections E and L are less than their free floats, and based on the analysis above, they only influences the construction periods of themselves; the delay time of bidding section B is more than its free float but less than its total float, with an effect on the earliest start time of the next bidding section, but with no effect on the construction period of the program; and the delay times of bidding sections M, G, and F are more than their total floats, having influence not only on the construction periods of themselves but also on the earliest start times of the next bidding section and other subsequent bidding sections as well as the construction period of the program.

The amounts of penalty for delay in bidding sections calculated with the penalty model presented in this paper are listed in Table 2.

Table 2 Penalty for delay in bidding sections of Baoying station program calculated with present penalty model

4.3 Results and discussion

Penalties for delay in the six bidding sections D, H, I, M, G, and F calculated with the present penalty model are all more than those calculated with the current penalty calculation method. The main reason is that the delay in bidding sections D, H, I, M, G, and F influences not only the construction periods of themselves but also the earliest start times of the next bidding section and other subsequent bidding projects and the construction period of the program.

Penalties for delay in bidding sections E, L, and B calculated with the present penalty model are all less than those calculated with the current penalty calculation method, as the delay in bidding sections E and L just influences the construction periods of themselves, andthe delay of bidding section B influences both the construction period of itself and the earliest start time of the next bidding section, but they have no influence on the construction period of the program.

Taking bidding sections B and M as examples, the contract amount of bidding section B is 8.87 times that of bidding section M. Although both of them are delayed by 120 d, the penalty for the former is only 1.84 times that for the latter. The main reason is that the delay in bidding section B only has influence on the construction period of itself and the earliest start time of the next bidding section, while the delay in bidding section M has influence not only on the construction period of itself and the earliest start time of the next bidding section but also on the construction period of the program. The same case occurs in bidding sections H and L.

5 Conclusions

(1) Compared with the current penalty calculation method, the present penalty model considers the influence of delay in a bidding section not only on the construction period of itself but also on the earliest start times of the next bidding section and other subsequent ones and the construction period of the program, and the amounts of penalty for delay in the critical and non-critical bidding sections are determined under different conditions. The present penalty model is more reasonable to reflect the losses caused by delay in bidding sections.

(2) If the delay in a bidding section only has influence on the construction period of itself, it is reasonable to calculate the penalty based on the contract amount of the bidding section; however, if the delay in a bidding section has influence not only on the construction period of itself, but also on the earliest start times of the next bidding section and other subsequent ones and the construction period of the program, the penalty for delay in the bidding section should be calculated with the present penalty model.

(3) In the penalty model given in this paper, the penalty rate can be obtained by the amount of penalty divided by the number of days delayed.

(4) The empirical results show that the greater the influence of delay in bidding sections on the program, the more reasonable the result obtained by the penalty model given in this paper.

The losses caused by delay in bidding sections are influenced by many factors, even involving multilateral game; thus, it is necessary to perform further study on the quantification of the losses from different aspects of projects by combining with their practical schedules to get more reasonable results.

Broome, J., and Perry, J. 2002. How practitioner set share fractions in objectives cost contract.International Journal of Project Management, 20(1), 58-64. [doi:10.1016/S0263-7863(00)00035-1]

Browning, T. R. 2001. Applying the design structure matrix to system decomposition and new directions.IEEE Transactions on Engineering Management, 48(3), 292-306.

Bubshait, A. A. 2003. Incentive/disincentive contracts and its effects on industrial projects.International Journal of Project Management, 21(1), 63-70. [doi:10.1016/S0263-7863(01)00078-3]

Federation International Des Ingenieursconseils (FIDIC). 1999.Conditions of Contract for Construction for Building and Engineering Works Designed by the Employer. International Federation of Consulting Engineers.

Feng, J. C., Hong, Y. Z., Zhang, J., Zhou, Z. B., Sun, W. J., and Wen, S. Y. 2010. Research on the life cycle of the program.Statistics and Decision, (9), 38-40. (in Chinese)

Feng, J. C., Li, L., Yang, N., Hong, Y. Z., Pang, M., Yao, X., and Wang, L. C. 2011. Research on construction of project critical chain model in South-to-North Water Diversion Project with multi-resource constraints based on portfolio technology.Water Science and Engineering, 4(2), 237-248. [doi:10.3882/ j.issn.1674-2370.2011.02.010]

He, Z. W., Xu, Y., and Zhu, S. Y. 2005. Study on project payment scheduling problems with bonus-penalty structure from two viewpoints.Systems Engineering—Theory and Practice, 25(10), 39-45. (in Chinese)

Pillai, A. S., Joshi, A., and Rao, K. S. 2002. Performance measurement of R&D projects in multi-projects concurrent engineering environment.International Journal of Project Management, 20(20), 165-177. [doi:10.1016/S0263-7863(00)00056-9]

Reiss, G., Anthony, M., Chapman, J., Leigh, G., Pyne, A., and Rayner, P. 2006.Gower Handbook of Programme Management. Aldershot: Gower Publishing Limited.

Tareghian, H. R, and Taheri, H. 2006. An application of randomized minimum cut to the project time/cost trade-off problem.Applied Mathematics and Computation, 173(2), 1200-1207. [doi:10.1016/j.amc.2005. 04.063]

Turner, J., Rodney, J., and Simister, S. J. 2000.Gower Handbook of Project Management. 3rd Ed. Aldershot: Gower Publishing Limited.

Wang, Y. L., and Yang, Y. H. 2005. Incentive optimization and the determination of optimal project duration to multi-contracts.Forecasting, 24(2), 60-63. (in Chinese)

Woodbine, G. F. 2004. Moral choice and the declining influence of traditional value orientations within the financial sector of a rapidly developing region of the People’s Republic of China.Journal of Business Ethics, 55(1), 43-60. [doi:10.1007/s10551-004-5592-5]

Zheng, W. Y. 2008.A Study on Incentive Mechanism of Construction Project Based on the Theory of Principal-agent. M. E. Dissertation. Tianjing: Tianjing University. (in Chinese)

(Edited by Ye SHI)

This work was supported by the National Science and Technology Plan of China (Major Project of the Eleventh Five-Year Plan, Grant No. 2006BAB04A13), the Philosophy and Social Science Fund of Education Department of Jiangsu Province (Grant No. 07SJD630006), the Third Key Discipline (Techno-Economics and Management) of the Project 211, and the Key Disciplines of Jiangsu Province (Engineering and Project Management).

*Corresponding author (e-mail:feng.jingchun@163.com)

Received Jul. 14, 2011; accepted Mar. 7, 2012